How do I model and animate a twinkling star?
Blender allows you to generate a Noise modifier for animations. This could give you a "twinkling" effect if you apply the noise to a material's value such as Emission, Intensity, Transparency, etc.

First, mouse-over the value you want to apply noise to. In this example I'm using Diffuse Intensity.



Then press I to add a keyframe. If it works, you'll see the button turn yellow.



Open the Graph Editor and click on the channel used for controlling the Intensity.

 

In the Graph Editor, open the Properties panel by either pressing N or selecting View >> Properties. Under Modifiers, click Noise. This will give you a set of controls to manipulate the pseudo-randomization of the Intensity. This works on any value that can be animated, including colors.